






'''simple docstring'''







import inspect
import os
import unittest

import torch

import accelerate
from accelerate import Accelerator
from accelerate.test_utils import execute_subprocess_async, require_multi_gpu
from accelerate.utils import patch_environment




class   __SCREAMING_SNAKE_CASE       (unittest.TestCase       ):


  """simple docstring"""


  def    _a       (			self	):






         """simple docstring"""


         a_						     =			inspect.getfile(accelerate.test_utils	)
         a_						     =			os.path.sep.join(mod_file.split(os.path.sep	)[:-1] + ['scripts', 'test_script.py']	)
         a_						     =			os.path.sep.join(
             mod_file.split(os.path.sep	)[:-1] + ['scripts', 'test_distributed_data_loop.py']	)
         a_						     =			os.path.sep.join(mod_file.split(os.path.sep	)[:-1] + ['scripts', 'test_ops.py']	)







  @require_multi_gpu
  def    _a       (			self	):






         """simple docstring"""


         print(f'Found {torch.cuda.device_count()} devices.'	)
         a_						     =			['torchrun', f'--nproc_per_node={torch.cuda.device_count()}', self.test_file_path]
         with patch_environment(omp_num_threads=1	):
                execute_subprocess_async(UpperCamelCase__   ,	env=os.environ.copy()	)







  @require_multi_gpu
  def    _a       (			self	):






         """simple docstring"""


         print(f'Found {torch.cuda.device_count()} devices.'	)
         a_						     =			['torchrun', f'--nproc_per_node={torch.cuda.device_count()}', self.operation_file_path]
         print(f'Command: {cmd}'	)
         with patch_environment(omp_num_threads=1	):
                execute_subprocess_async(UpperCamelCase__   ,	env=os.environ.copy()	)







  @require_multi_gpu
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			['torchrun', f'--nproc_per_node={torch.cuda.device_count()}', inspect.getfile(self.__class__	)]
         with patch_environment(omp_num_threads=1	):
                execute_subprocess_async(UpperCamelCase__   ,	env=os.environ.copy()	)







  @require_multi_gpu
  def    _a       (			self	):






         """simple docstring"""


         print(f'Found {torch.cuda.device_count()} devices, using 2 devices only'	)
         a_						     =			['torchrun', f'--nproc_per_node={torch.cuda.device_count()}', self.data_loop_file_path]
         with patch_environment(omp_num_threads=1   ,	cuda_visible_devices='0,1'	):
                execute_subprocess_async(UpperCamelCase__   ,	env=os.environ.copy()	)


if __name__ == "__main__":
  __lowerCAmelCase        =							Accelerator()
  __lowerCAmelCase        =							(accelerator.state.process_index + 2, 10)
  __lowerCAmelCase        =							torch.randint(0, 10, shape).to(accelerator.device)

  __lowerCAmelCase        =							""

  __lowerCAmelCase        =							accelerator.pad_across_processes(tensor)
  if tensora.shape[0] != accelerator.state.num_processes + 1:
    error_msg += f"Found shape {tensora.shape} but should have {accelerator.state.num_processes + 1} at dim 0."
  if not torch.equal(tensora[: accelerator.state.process_index + 2], tensor):
    error_msg += "Tensors have different values."
  if not torch.all(tensora[accelerator.state.process_index + 2 :] == 0):
    error_msg += "Padding was not done with the right value (0)."

  __lowerCAmelCase        =							accelerator.pad_across_processes(tensor, pad_first=True)
  if tensora.shape[0] != accelerator.state.num_processes + 1:
    error_msg += f"Found shape {tensora.shape} but should have {accelerator.state.num_processes + 1} at dim 0."
  __lowerCAmelCase        =							accelerator.state.num_processes - accelerator.state.process_index - 1
  if not torch.equal(tensora[index:], tensor):
    error_msg += "Tensors have different values."
  if not torch.all(tensora[:index] == 0):
    error_msg += "Padding was not done with the right value (0)."

  # Raise error at the end to make sure we don't stop at the first failure.
  if len(error_msg) > 0:
    raise ValueError(error_msg)












'''simple docstring'''







from math import isqrt, loga


def       __UpperCamelCase					(      lowercase_       :  int   ):
       """simple docstring"""




       a_						     =			[True] * max_number
       for i in range(2   ,       isqrt(max_number - 1   ) + 1   ):
              if is_prime[i]:
                     for j in range(i**2   ,       lowercase_   ,       lowercase_   ):
                            a_						     =			False

       return [i for i in range(2   ,       lowercase_   ) if is_prime[i]]


def       __UpperCamelCase					(      lowercase_       :  int = 800_800   ,       lowercase_       :  int = 800_800   ):
       """simple docstring"""




       a_						     =			degree * loga(lowercase_   )
       a_						     =			int(lowercase_   )
       a_						     =			calculate_prime_numbers(lowercase_   )

       a_						     =			0
       a_						     =			0
       a_						     =			len(lowercase_   ) - 1
       while left < right:
              while (
                  prime_numbers[right] * loga(prime_numbers[left]   )
                  + prime_numbers[left] * loga(prime_numbers[right]   )
                  > upper_bound
              ):
                     right -= 1
              hybrid_integers_count += right - left
              left += 1

       return hybrid_integers_count


if __name__ == "__main__":
  print(f"""{solution() = }""")




